A192660 Floor-Sqrt transform of Lucas numbers (A000032).

1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 11, 14, 17, 22, 29, 36, 46, 59, 76, 96, 122, 156, 199, 253, 321, 409, 521, 662, 842, 1072, 1364, 1735, 2206, 2807, 3571, 4542, 5777, 7349, 9349, 11892, 15126, 19241, 24476, 31133, 39602, 50375, 64079, 81509, 103681, 131885

Offset: 0

Author

Emanuele Munarini, Jul 07 2011

Keywords

• nonn

Comments

This is the same as the floor-sqrt transform of phi^n, where phi = (1+sqrt(5))/2.

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000

Programs

Magma

[Floor(Sqrt(Lucas(n))): n in [0..50]]; // Vincenzo Librandi, Sep 30 2017

Mathematica

Table[Floor[Sqrt[LucasL[n]]], {n,0,100}]

Maxima

makelist(floor(sqrt(fib(n-1)+fib(n+1))),n,0,24);

PARI

a(n) = sqrtint(fibonacci(n-1)+fibonacci(n+1)); \\ Michel Marcus, Sep 30 2017

Formula

a(n) = floor(sqrt(Lucas(n))).